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Is there some reasonably accurate ballparking formula to allow for quick conversions between IAS and TAS as a function of pressure altitude and difference of ground temperature relative to standard atmosphere? That is,

E.g. "for each 1,000ft subtract X%, for each degree F/C subtract Y%" so that if I'm at 8,000ft and ground temperature is 10 C, I simply subtract 8X% and add 5Y% to get a good approximation.

My idea is to have a quick ballpark to start working with, in case there is no time to start fiddling with the flight computer, or in cases where the error would be insignificant for practical purposes.

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    $\begingroup$ Is there a certain range of airspeeds/altitudes you are interested in? The relationships are not linear, so higher altitudes and and supersonic speeds will change the calculation. $\endgroup$ – fooot Nov 21 '17 at 18:53
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    $\begingroup$ I came up with a rough figure of +1.7% of CAS for each 1000ft, and +/-1% for each +/-5 degrees of ISA delta from playing with this calculator. $\endgroup$ – fooot Nov 21 '17 at 19:10
  • $\begingroup$ @SteveKuo For all GA airplanes that I am familiar with, Calibrated and Indicated Airspeed are the same at cruise. It is usually only with flaps and low speed that they differ. $\endgroup$ – JScarry Nov 21 '17 at 21:14
  • $\begingroup$ @JScarry Perhaps then question should have been phrased "CAS vs TAS" $\endgroup$ – Steve Kuo Nov 21 '17 at 21:16
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As @Adam cites, Ed Williams has put together a nice aviation formulary. So I won't consult it in this quick answer, which I use as a rule of thumb only.

To ballpark TAS, for every 1000ft increase CAS (or IAS) by 2%.

That is a ballpark, and it, for example, will not work when you are flying a U-2 at 70,000 feet.

Addendum: Many aircraft have a sliding wheel on the ASI (Airspeed Indicator) which will allow you to move a TAS scale around the bezel of the instrument. For anyone wanting more precision than a ballpark rule, you might consider: http://www.dtic.mil/dtic/tr/fulltext/u2/a280006.pdf

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  • $\begingroup$ Although it is always quoted as TAS = CAS + 2% for every 1000FT, wouldn't it be more accurate to say TAS = CAS + 2% for every 1000FT of pressure altitude? After all, we are correcting for variations from the ISA. $\endgroup$ – jumblie Mar 31 at 8:53
  • $\begingroup$ @jumblie, in what circumstances would you expect a significantly non-linear pressure lapse rate? In general above some altitude, say 10,000 feet the 1000 foot guidance gets substantially off, because of the atmospheric density distribution with altitude. So the refined use of pressure altitude is unnecessary and implies more accuracy in the rule of thumb than really exists. $\endgroup$ – mongo Mar 31 at 13:54
  • $\begingroup$ I wasn't necessarily thinking non-linear (though use of pressure altitude would mitigate that too), but anything where the pressure lapse rate deviates from the norm such as extreme temperatures. $\endgroup$ – jumblie Apr 1 at 2:47
  • $\begingroup$ Well the question was for a ballpark, and I figure that a ballpark figure is something one can easily do in their head. A student can do the calculation in their head, and it is reasonably accurate. But adding the refinement of pressure altitude increases the complexity. If one was creating a calculator for TAS and CAS, then there are several refinements that can be made, and I agree with you on pressure altitude for that, and the NASA paper cited develops a refined model. We just diverge on the reliance of pressure altitude for a ballpark rule. $\endgroup$ – mongo Apr 1 at 13:48
  • $\begingroup$ Thanks @Mongo for clarifying that pressure altitude would indeed be more accurate albeit less practical. I agree with your thoughts. The reason I brought it up in the first instance was to check that my understanding of what was going on was correct. $\endgroup$ – jumblie Apr 2 at 3:14
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Indicated vs. True is a hard one, as every aircraft has an instrument error and a position error. Once calibrated into Calibrated Air Speed however, this document gives CAS as a function of TAS:

enter image description here

All of them more or less straight lines, gradients a function of the altitude.

For temperature: the rule of thumb of density altitude can be used. From this website:

Keep in mind the standard temperature is 15 degrees C but only at sea level. It decreases about 2 degrees C (or 3.5 degrees F) per 1,000 feet of altitude above sea level. The standard temperature at 7,000 feet msl, therefore, is only 1 degree C (or 34 degrees F).

So the procedure is:

  • Convert pressure altitude with temperature deviation. Ground temperature = 10 °C so density altitude = (10 - 15) * (1000/2) = -2,500 ft
  • Find TAS at 30,000 ft by subtracting 2,500 ft, then applying the TAS thumb rule of 2% / 1,000 ft: TAS @ 27,500 ft = 27,500 * (1.02/1,000) = 1.55 CAS.

At 30,000 ft and ground temperature of 10°C , TAS = 1.55 * CAS

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  • $\begingroup$ Good equations for that kind of thing here: edwilliams.org/avform.htm#Mach $\endgroup$ – Adam Nov 22 '17 at 15:43
  • $\begingroup$ Ed was working on that formulary in 1980, when I was working with him. He has maintained, and refined, that reference for many years. $\endgroup$ – mongo Nov 22 '17 at 23:57

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